Description: This technical analysis article introduces the
Fibonacci sequence and Golden Ratio in Elliott Wave Theory as a useful
technique for trading Forex.

In the 1940’s, R.N. Elliott enhanced his initial Wave Theory
tenets to include the ratios between Fibonacci numbers that have now become one
of the more popular Forex indicators used by traders.

Elliott made this change because he noted that the mass
psychology underlying the markets’ movements displayed a tendency to repeat
over time, and that they did so in numbers of waves that were included in the
Fibonacci sequence.

As a result of this observation, he postulated that this
phenomenon could be related to an important sequence of numbers that the
mathematician Fibonacci
tied to the reproductive increase of a theoretical population of rabbits.

Computing the
Fibonacci Sequence

In the book Liber Abaci, published
in the 13th century, Italian mathematician Leonardo Pisano Bigollo (who was also known as Fibonacci) posed a question
regarding the reproduction of rabbits that went roughly as follows:

“How many
pairs of rabbits will be produced in a year, beginning with a single pair, if
in every month each pair bears a new pair which becomes productive from the
second month on?”

Producing the answer to this question involves calculating
what is now known as the Fibonacci sequence. Basically, to generate the
Fibonacci sequence, you can perform the following steps:

(1)Start with
a pair of immature rabbits, one male and one female.

(2)Then you
wait one month before breeding them.

(3)Then you wait
one month for them to have a pair of babies - one girl and one boy.

(4)Then you
wait one month when the original pair have babies, but their babies do not.

(5)Then you
wait one month when the original pair have babies, and so do their first set of
babies, but not their second set.

(6)Repeat the
process over and over and over again until you get tired.

(7)Assume that
no rabbits die.

(8)Count how
many pairs of rabbits there are at the end of each month.

Steps (1) and (2) generate the first two numbers in the
sequence, which are 1 and 1.

Step (3) generates the next number which
is 2 (one original pair and one pair of baby rabbits of the opposite sex).

Step (4) generates the next number which
is 3 (one original pair, their first pair of babies, and a second pair of babies
from the original pair).

Step (5) generates the next number which
is 5 (one original pair, their first pair of babies, their second pair of
babies, and a new pair of babies from the original pair and the first pair of
babies.)

This process can then be repeated indefinitely.

Eventually, you might notice an important short cut, which
is that you can simply compute the current number of rabbit pairs by adding
together the previous two numbers.This generates the infinite Fibonacci
sequence as follows:

1, 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 144…

In which the sequence is created numerically by taking 1 and
1, and then adding them together to make 2, and then adding 1 and 2 together to
make 3, and so on.

Fibonacci Sequence
Ratios and the Golden Mean

Interestingly, as this famous numerical sequence progresses,
a very unusual thing happens. The ratio of one number divided
by the next number in the sequence approximates 0.618, which yields roughly
1.618 when inverted.

This is known as the so-called Golden Mean or Golden Ratio,
and mathematicians have found the fact that these two numbers, which are
reciprocals of each other, have the same three decimal places to be rather
fascinating. Furthermore, numerous theories about the significance and power of
this numerical phenomenon have been proposed.

Even more interesting is the observation that the ratio of
one number to that seen two further in the sequence approaches 0.382, while
three further approaches 0.236.

Here is a further mathematical look at the Fibonacci Sequence and the Golden Ratio:

Using Fibonacci
Ratios in Elliott Wave Theory

With the addition of the ½ or 0.5 ratio, and also the
(1-0.236) = 0.764 ratio used by some analysts, the popular technical analysis
technique of computing Fibonacci retracements was ready to be included by
Elliott as part of his Wave Theory:

First of all, Elliott noted that market movements or waves
tended to occur in sets of Fibonacci numbers. Elliott also observed that major
market moves would tend to be corrected by a degree that approximated a
Fibonacci ratio.

Accordingly, by first multiplying the extent of the initial
move by these ratios and then projecting them in the opposite direction from
that move off of the final price of the move, he proposed that traders could
compute a series of likely Fibonacci retracement
targets.

Furthermore, Elliott noted that impulsive waves in an
unfolding trend tend to relate to each other either on a 1:1 or 1:2 ratio, or
by adding the Fibonacci ratios, to get 1:1.236, 1:1.382, 1:1.5, 1:1.764 and so
on. These form the set of Fibonacci projection ratios.

By using these ratios calculated for an observed impulse,
Fibonacci projections can then be computed off of the end of an intervening
correction to determine the likely extent of a subsequent impulse. While this
projection technique can be helpful in providing targets when one impulse is
known, it can be even more accurate when two impulses have already occurred.

Some Forex
traders using Elliott
Wave Theory also successfully apply the Fibonacci projections to obtaining
targets for the C wave of three wave corrections once the A and B waves have
finished unfolding. Forex stands for Foreign Exchange
and this currency trading market is the fastest growing, largest exchange in
the whole world. A Forex trader's objective is to
make money by trading one currency for another. The process is very risky and
it is a wise choice to make sure you do your research before you attempt to
invest in this network.

*Jennifer Gorton is the content manager of ForexIndicators.net. Her main task is to make sure all the articles on her site are very educational
and useful while also planning out new sections for more advanced trading tool information. She has recently expanded her knowledge on the
mathematical aspects of her indicators and is quite thrilled to share the information she's discovered.